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It's because of inharmonicity in the harmonics of the fundamental tones. They cannot be exact mathematic multiples due to wire stiffness. You would notice this especially in shorter pianos(like the Yamaha CP70 so that that it's virtually impossible to tune all those harmonics in the same octave beatless).

All the electronic tuning aids take this into account in tuning. My particular machine(the Verituner 100)takes into account even more of the harmonics than the others do when determining what the correct frequency of each note is.

Hi David: Let me try to explain the phenomenon of "stretching octaves" in piano tuning. I'm sure there will be others after me doing a better job of explaining, but here goes. This is how I explain this to customers: Tuning each note in a piano to the exact frequency of that note will result in a "dead" sound, much like that of a harpsicord. Not to say its a bad sound, just different than what we expect a piano to sound like. By stretching or tuning very slightly off pitch, we give the piano "color." We cause notes to interact with each other in a way that makes a full, rich complex tone when chords are played. Describing sounds and tones are hard to put into words, but you get the idea. Its sort of like looking at a black and white television if you're used to color. The picture is there, but there is a lot missing. The "palette" of music created by a properly tuned piano is the color in a TV. Hope this helps. PNO2NER.

What PNO2ER had to say was verified many years ago according to an article I read in the PTG Journal. It said that when a piano was actually constructed that had zero inharmonicity it had a dead sort of sound. But how they would have been able to accomplish this with wire having no stiffness(that creates the inharmonicity effect)is beyond me. Maybe I mis-read and it was only a "virtual" piano.

Far be it for me not to try and confuse things. I’d throw into the mix that since each string, and particularly the bass strings, really sound more than just one note, you have to try and tune those upper notes (partials) with their equivalents, which are actually found on up the keyboard. The ‘C’ below middle ‘C’, for example, sounds numerous partials. Its second partial would be a fifth above middle ‘C’, or ‘G’. Unstretched, the ‘G’ heard in that tennor ‘C’ is going to be sharp to the actual ‘G’ found a fifth above middle ‘C’. In order to tune the two together, one has to stretch the lower note further flat from what would be its “perfect” distance from the middle of the keyboard. “Ringing” of broad chords struck accross the piano is, to me, an indication that most of the inharmonicities in the bass have been well balanced with those, more fundamental, frequencies found in the treble.

I should think you’d have to violate the laws of physics to make a strung piano without any inharmonicities. Isn’t stiffness always part of the equation and a fundamental characteristic of wire?

I am impressed enough with Tunelabs. Even when I resample notes, the measured frequencies of the partials are nearly the same. I hope the same mistake isn’t being made each time, but am much happier with the results than those of the last tuner, who stretched things so far that playing on top of recordings meant a clearly sharp treble and a flat bass.

I’ve read people who equate stretch with “coloring” a piano’s tune. In a matter of speaking, I’ve also seen on the PTG board instances where making unisons slightly less than perfect is attempted to bring character to the sound. At best, I’d call it the introduction of a really slow beat that gives the tone some additional envelope. In each case you have to reconcile that an ETD can not make such subjective inputs into the tuning process with whether they are desireable in the first place.

From a guy that can't use a screwdriver without an instruction book. . . :rolleyes:

I read an article a long time ago, something about the fact that the nodes of a wave do not vibrate, therefor the string lenght and multiples (harmonics) expressed mathematically are not actual results when dealing with the physical properties of something like a vibrating piano string. Since physical space is lost, consequent adjustments in higher strings must be made to make the result pleasing to the human ear.

Consider the ratio of the string's diameter to its length. A harpiscord has very thin stringes in relation to the string's length. The nodal points where the partials occur are infinitessimal. (They occupy no space) A piano string is so thick compared to its length that it vibrates more like a steel bar rather than a string. Therefore its nodal points DO occupy space. This means that the upper partials of a given note will be higher than the mathemetical perfection. Let's say for example that C4 (middle C) is 200hz. that means that C6 should be 800hz.BUT... the C6 partial IN C4 is 802.3 hz. That means you have to tune C4 to 802.3 in order for it to be in tune with C4. and that's only 2 strings! . a piano has over 200 :p . have fun........

I gues after reading all of them I can make the following conclusions:

Stretch tuning can be likenned to a choir of singers. It seems the more relative variance in pitch you have, the richer the resulting sound (that is if the singers can sing reasonably in tune with each other.)

As far as the original perfectly tuned piano sounding dead goes, I guess this can be like comparing the sound of hammond organ with and without a leslie speaker in slow rotor mode. Anyone who has heard this will know that the one with a rotaing leslie speaker would sound much richer. Even though this particular (stretch) in tuning is done via the dopler effect the result is the same as having the notes slightly detuned from each other. In the world of the electric guitar this effect would be reproduced by the infamous chorus pedal.

This is a good question and even though any piano technician should know the answer, many don't. You received some good answers from other readers. Inharmonicity is the reason octaves cannot be tuned perfectly purely and that even the middle octave should be stretched out.

There is another, more enigmatic reason why the top octaves can be stretched quite a bit in many cases. The human perception or "ear", if I may, simply wants to hear octaves and higher notes much sharper than they should be theoretically.

In one sense, you really can't tune the treble too sharp but of course, there are consequences to every decision made about tuning. Every attempt at pleasing the "ear" with melodically high pitch must be moderated with what that does to other intervals and chords which may be played.

You mentioned the "Standard" scale in your post. There is a lot of misunderstanding about that. It is really only a set of numbers created by multiplying and dividing the number 440 by the 12th root of 2. It provides a convenient paradigm from which all real tuning can be measured but should never be considered to be "perfect" or a goal in itself.

See my website for some real insights into current thinking about tuning, temperament and octave stretching.